In fact, the study of lower bounds for \(\lambda _1^*(Y)\)  for hyperbolic three-manifolds (not necessarily rational homology spheres) has recently attracted a lot of attention in light of its role in a conjecture on Bergeron and Venkatesh on the growth of torsion in the homology of congruence covers of a fixed arithmetic manifold [1]}. Interesting work providing lower bounds in terms of geometric quantities describing the areas of surfaces with boundary given curves can be found in [2]}, [3]} and [4]}. Lower bounds of a different nature were provided in [5]}.
